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Descartes, René
Descartes, René (Latinized name, Renatus Cartesius). Born at La Haye in Touraine on May 31, 1596; died inStockholm on Feb. 11, 1650. French philosopher and mathematician. Descartes was a member of an old noble family and was educated at the Jesuit school of LaFleche in Anjou. At the beginning of the Thirty Years’ War he served in the army, which he left in1621. After traveling for a few years, he settled in 1629 in the Netherlands, where he spent 20 yearsin seclusion engaged in scientific studies. There he published his main works, Discourse on Method(1637; Russian translation, 1953), Meditations on First Philosophy (1641; Russian translation,1950), and Principles of Philosophy (1644; Russian translation, 1950). In 1649, at the invitation ofQueen Christina of Sweden, he went to Stockholm, where he died soon afterward. The main feature of Descartes’s philosophy is the dualism of soul and body—of thinking substanceand extended substance. In identifying matter with extension, Descartes considers it not so muchas physical substance but rather as stereometric space. In contrast to the medieval concept of afinite world and of qualitative diversity of natural phenomena, he affirms that the world’s matter(space) is limitless and homogeneous; it has no voids and can be endlessly divided. This theorycontradicts classical atomism, revived in Descartes’s time, which considered the world asconsisting of indivisible particles separated by voids. Descartes considered each particle of matteran inert and passive mass. Motion, which Descartes reduced to the displacement of bodies, wasalways the result of an impulse given by one body to another. The universal cause of motion inDescartes’s dualist conception is god, who created matter together with motion and rest andpreserves them. Descartes’s teachings on man are also dualist. Man is the real union of the soulless and lifelessbodily mechanism and the soul, which possesses thought and will. The interaction between bodyand soul takes place as a result of a special organ, the pineal gland. Descartes placed the will firstamong the faculties of the human soul. The main action of the affects, or passions, is to incline the soul to want those things for which thebody is prepared. God himself has united body and soul, thereby distinguishing man from animals.Descartes denied the existence of consciousness in animals. Since they were automatons withoutsouls, they could not think. The human body, like the body of animals, is merely a complexmechanism formed out of material elements and capable, as a result of the mechanical effect ofthe objects around it, of performing complex movements. Descartes studied the structure of various organs of animals and of their embryos at differentstages of their development. His physiological works are based on the teachings of W. Harvey onthe circulation of the blood. He was the first to try to explain the nature of voluntary and involuntarymovements and described the system of reflex movements in which the centripetal and centrifugalparts of the reflex arc are distinguished. Descartes regarded not only the contraction of the skeletalmuscular system but also many vegetative acts as being reflex movements. Among the philosophical questions that Descartes studied, the most significant was that of themethod of knowledge. Like F. Bacon he considered the ultimate purpose of knowledge to be man’smastery over the forces of nature, the discovery and invention of technical methods, the knowledgeof causes and effects, and the betterment of the nature of man himself. Descartes seeks theabsolutely certain fundamental point of departure for all knowledge and a method that makes itpossible, by basing oneself on this point of departure, to build an equally certain edifice of allknowledge. He does not find such a point of departure or such a method in scholastic philosophy.For that reason the point of departure in Descartes’s philosophical thought is doubt of the truth ofgenerally accepted knowledge, including all existing forms of knowledge. However, as in the caseof Bacon, Descartes’s initial doubting is not the conviction of an agnostic but merely a preliminarymethodological technique. I may doubt the existence of a world outside myself and even theexistence of my own body. However, my own doubting does in any case exist, and doubting is anact of thinking. I doubt inasmuch as I think. If doubting is an established fact, then it must existinsofar as thought exists and insofar as I exist myself as a thinking being: “I think, therefore I am”(Sobr. soch., Moscow, 1950, p. 282). Descartes’s idealism is linked to the religious premises of his system. To prove the reality of theexistence of the world, Descartes considers it essential to prove first the existence of god. Heconstructs his proof on the model of the ontological proof of the existence of god given by Anselmof Canterbury. And if god exists, then his perfection excludes the possibility that he could deceiveus. Consequently, the existence of the objective world is also beyond doubt. In his teaching on knowledge, Descartes was the founder of rationalism, which developed from theobservation of the logical character of mathematical knowledge. Mathematical truths, according toDescartes, are beyond all doubt, and possess a universality and necessity inherent in the nature ofthe intellect itself. Consequently, Descartes attributed an exceptionally important role to theprocesses of deduction, by which he understood reasoning based on completely certain points ofdeparture (axioms) and consisting of a chain of equally certain logical deductions. The certainty ofthe axioms is perceived by the mind intuitively, with full clarity and distinctness. For a clear anddistinct understanding of the whole chain of deductions, a strong memory is required. Consequently, immediately evident points of departure, or intuitions, are preferable to deductive judgments. Equipped with the right means for thinking—intuition and deduction—the mind may attaincompletely certain knowledge in all fields, provided that it is guided by the right methods. The rulesfor Descartes’s rationalist method consist of the four following precepts: (1) never accept anythingas true unless it is recognized to be certainly and evidently such and unless it presents itself soclearly and distinctly that there can be no reason for doubting its truth; (2) divide each complexproblem into its component parts; (3) proceed in an orderly fashion from what is known and provedto what is not known and not proved; (4) allow for no omissions in the logical chain of reasoning.The perfection of our knowledge and its extent are determined according to Descartes by theexistence in us of innate ideas, which he divides into innate conceptions and innate axioms. Verylittle is known for certain about physical things; we know considerably more about the human spiritand even more about god. The teachings of Descartes and the trends in philosophy and the natural sciences that carried onhis ideas were given the name Cartesianism, from the Latinized form of his name. He exertedconsiderable influence on the subsequent development of science and philosophy, both materialistand idealist. Descartes’s teachings on the immediate certainty of self-consciousness, on innateideas, on the intuitive nature of axioms, and on the opposition of the material and the ideal laid thefoundation for the development of idealism. On the other hand his teachings on nature and hisgeneral mechanistic method make his philosophy one of the milestones of the modern materialistconception of the world. V. F. ASMUS In his Geometry (1637), Descartes introduced the concepts of variable and function. He considereda variable in two ways: as a line segment of variable length and constant direction—the hangingcoordinate of a point whose motion describes a curve—and as a continuous numerical variable thatruns through the set of values representing that line segment. This twofold treatment of a variableresulted in an interweaving of geometry and algebra. Descartes treated a real number as the ratio ofany line segment to the unit segment, although such a definition for real numbers was explicitlystated much later by I. Newton; negative numbers were given a real interpretation in Descartes’swork as directed ordinates. He greatly improved the existing system of notation, introducing thenow familiar symbols for variables (x, y, z , …) and coefficients (a, b, c, …), as well as the notationfor powers (x4, a5, …). His style for writing formulas was almost identical with the style in usetoday. Descartes laid the foundations for a number of investigations into the properties of equations: heformulated the rule of signs for determining the number of positive and negative roots, raised thequestion of the boundaries of real roots, propounded the problem of reducibility (the representationof an entire rational function with rational coefficients as the product of two functions of the samekind), and indicated that a third-degree equation can be solved in terms of quadratic radicals and issolvable with ruler and compass when it is reducible. In analytic geometry, which P. Fermat developed at the same time as Descartes, Descartes’s mainachievement was his system of coordinates. He included within the field of geometric studies thestudy of “geometric” curves (later called algebraic curves by Leibniz), which can be described bythe movements of hinged mechanisms. Transcendental (“mechanical”) curves are excluded fromDescartes’s geometry. In his Geometry he described a method for constructing normals andtangents to plane curves (in connection with investigations on lenses) and applied the method, inparticular, to certain fourth-order curves, the so-called Cartesian ovals. Although he laid the foundations of analytic geometry, he himself did not advance very far into thefield: he did not consider negative abscissas and did not touch upon the problems involved in theanalytic geometry of three-dimensional space. Nevertheless, the Geometry had a tremendousinfluence on the development of mathematics. Descartes’s correspondence also includes otherdiscoveries: he calculated the area of the cycloid, showed how to draw tangents to the cycloid, anddetermined the properties of the logarithmic spiral. From his manuscripts it is clear that he knew therelation (subsequently discovered by L. Euler) between the numbers of faces, vertices, and edgesof convex polyhedra. WORKS Oeuvres. Edited by C. Adam and P. Tannery. Vols. 1–12 (with supplement). Paris, 1897–1913. Correspondance. Edited by C. Adam and G. Milhaud. Vols. 1–6. Paris, 1936–56. In Russian translation. Soch., vol. 1. Kazan, 1914. Izbrannye proizvedeniia. Moscow 1950. Geometriia. Moscow-Leningrad, 1938. (Includes selected works of P. Fermat and selected letters ofDescartes.) REFERENCES Wieleitner, H. Istoriia matematiki ot Dekarta do serediny 19 stoletiia, 2nd ed. Moscow, 1966.(Translated from German.) Liubimov, N. A. Filosofiia Dekarta, St. Petersburg, 1886. Fouillée, A. Dekart. Moscow, 1895. (Translated from French.) Fischer, K. Istoriia novoi filosofii, vol. 1: Dekart, ego zhizn’, sochineniia i uchenie. St. Petersburg,1906. (Translated German.) Spinoza, B. Printsipy filosofii Dekarta. Moscow, 1926. Bykhovskii, B. E. Filosofiia Dekarta. Moscow-Leningrad, 1940. Asmus, V. F. Dekart. Moscow, 1956. Laporte, J. Le Rationalisme de Descartes. Paris, 1945. Lefèvre, R. La Vocation de Descartes, part 1. Paris, 1956. Alquié, F. Descartes. Paris, 1963. Sebba, G. Bibliografia cartesiana. The Hague, 1964.